Hello :
let A(0,3,2) and (Δ) this line , v vector parallel to (<span>Δ).
M</span>∈ (Δ) : vector (AM) = t v..... t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector <span>perpendicular
to the plane : n </span>⊥ v .... n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v .... vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) <span>perpendicular to (1,1,1)
</span>because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
-8x+14≥60 or -4x+50<58
-8x≥46 or -4x<8
x≤ -23/4 or x>-2
A is correct.
The probability of three independent events happening one after the other is the multiplication of the probability of the single events.
The probability of spinning an odd number is 5/10=1/2, because there are 5 odd numbers (1,3,5,7 and 9) out of the 10 numbers from 1 to 10.
The probability of spinning a number less than 4 is 3/10, because there are 3 numbers (1,2 and 3) that are less than 4 out of the 10 numbers from 1 to 10.
The probability of spinning a 7 is 1/10, because you only have one good outcome out of 10.
So, the probability of winning the game is
Answer:
(a)29
(b)91cm
(c)13cm
Step-by-step explanation:
(a)From the graph, 11 men have a waist measurement of 85cm and below.
Since the cumulative frequency is 40
Number of men who have a waist measurement of more than 85 cm
(b)Median
Tracing 20 from the y-axis to the x-axis, the median waist measurement is 91cm.
(c)Interquartile Range
Interquartile Range = 
From the graph, at y=10, x=84 cm
From the graph, at y=30, x=97 cm
Therefore:
Interquartile Range=97-84=13cm
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10. Then the correct option is B.
<h3>What is polynomial?</h3>
A polynomial expression is an algebraic expression with variables and coefficients.
The polynomial is given below.
5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷
Then polynomial can be arranged as
⇒ 6st⁹ + 5s⁶t² – 8s⁶t² – 6t⁷
⇒ 6st⁹ – 3s⁶t² – 6t⁷
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10.
Then the correct option is B.
More about the polynomial link is given below.
brainly.com/question/17822016
#SPJ1
